1 00:00:00,690 --> 00:00:01,560 ‫Welcome back. 2 00:00:02,070 --> 00:00:09,330 ‫I hope you have thought about how to obtain this form for our constraints, as mentioned before, you 3 00:00:09,330 --> 00:00:10,800 ‫have this equation here. 4 00:00:11,400 --> 00:00:16,980 ‫You know that x global tilde, it equals all that. 5 00:00:17,640 --> 00:00:24,540 ‫But let's not only focus on this one here, your excellent tilde equals all that. 6 00:00:25,050 --> 00:00:30,870 ‫And so how would you extract the last three elements from this vector? 7 00:00:31,500 --> 00:00:41,640 ‫Well, we can use a similar matrix that we used in order to extract states that we wanted to have as 8 00:00:41,640 --> 00:00:42,420 ‫outputs. 9 00:00:43,020 --> 00:00:45,750 ‫For that, we used this see matrix. 10 00:00:46,410 --> 00:00:53,160 ‫But now we have an augmented state vector and we want to extract different things from there. 11 00:00:53,730 --> 00:00:58,140 ‫We want to extract you two zero, use three zero and you for zero. 12 00:00:58,680 --> 00:00:59,970 ‫And you can do it like this. 13 00:01:00,690 --> 00:01:02,430 ‫This is what you want to have. 14 00:01:03,000 --> 00:01:04,920 ‫You want to have this vector. 15 00:01:05,550 --> 00:01:10,580 ‫Then this vector here, that's your X1 till there. 16 00:01:11,250 --> 00:01:16,950 ‫And so you want to extract this element, this element, and also this element. 17 00:01:17,550 --> 00:01:19,920 ‫Therefore, you need a matrix here. 18 00:01:20,550 --> 00:01:22,260 ‫And this matrix looks like this. 19 00:01:22,920 --> 00:01:27,240 ‫This one here, it will extract you two zero for you. 20 00:01:27,990 --> 00:01:36,000 ‫This one here it will extract you three zero for you and this one here it will extract you four zero 21 00:01:36,000 --> 00:01:36,420 ‫for you. 22 00:01:37,050 --> 00:01:41,550 ‫And so let's called this matrix C tilde asterisk. 23 00:01:42,210 --> 00:01:52,350 ‫OK, but now you want to extract you two Q3 and Q4 from Excel, the two X2, the three and X2, the 24 00:01:52,350 --> 00:01:53,370 ‫four as well. 25 00:01:53,940 --> 00:01:56,580 ‫Well, how about if I do this trick? 26 00:01:57,240 --> 00:01:59,220 ‫This is my ex till the global. 27 00:01:59,850 --> 00:02:01,020 ‫It's this one here. 28 00:02:01,680 --> 00:02:06,700 ‫If I now create this matrix here, then this is what I will have. 29 00:02:07,260 --> 00:02:09,480 ‫I will have this thing here. 30 00:02:10,110 --> 00:02:11,850 ‫This c till the star. 31 00:02:12,540 --> 00:02:14,430 ‫That's this matrix here. 32 00:02:15,000 --> 00:02:22,920 ‫So if you think about the dimensions, then this vector has three rows and one column this vector here 33 00:02:23,550 --> 00:02:26,460 ‫it has nine rows and one column. 34 00:02:27,090 --> 00:02:32,310 ‫And so this matrix here it has three rows and nine columns. 35 00:02:32,940 --> 00:02:42,750 ‫And now I create a global C till the star like this, and it consists of these little C to the stars 36 00:02:42,750 --> 00:02:43,140 ‫here. 37 00:02:43,770 --> 00:02:47,310 ‫So for example, this one here, it's this one here. 38 00:02:47,910 --> 00:02:50,400 ‫Three rows and nine columns. 39 00:02:50,610 --> 00:02:51,810 ‫The same thing here. 40 00:02:52,410 --> 00:02:57,300 ‫This one, this one and this one, all of them are the same. 41 00:02:57,900 --> 00:03:06,390 ‫And of course, that also means that these zero matrices, they have three rows in nine columns. 42 00:03:06,990 --> 00:03:14,400 ‫And so if you position these small seats, all the stars along the diagonal here and then you multiply 43 00:03:14,400 --> 00:03:20,040 ‫this C to the Star Global by this x still that global vector. 44 00:03:20,640 --> 00:03:25,710 ‫Then the result is that each predicted augment the state vector. 45 00:03:26,340 --> 00:03:33,900 ‫It will be multiplied by this C tilde star matrix like this in this order. 46 00:03:34,560 --> 00:03:41,910 ‫That means that you will be able to extract you two you three u four from all of these vectors. 47 00:03:42,510 --> 00:03:44,460 ‫And so I'm going to name this one. 48 00:03:45,120 --> 00:03:46,740 ‫Why Star Global? 49 00:03:47,370 --> 00:03:52,980 ‫And so if I write it out, then this is how it looks like this one here. 50 00:03:53,640 --> 00:03:59,100 ‫It's this one here, and we can call it y one star. 51 00:03:59,730 --> 00:04:03,150 ‫Then this one here it will be this one here. 52 00:04:03,750 --> 00:04:06,480 ‫We can call it y two star. 53 00:04:07,080 --> 00:04:10,500 ‫Then this one here it will be this one here. 54 00:04:11,160 --> 00:04:16,380 ‫That's why three star and finally, this one here. 55 00:04:17,010 --> 00:04:18,690 ‫Well, it's going to be this one here. 56 00:04:19,260 --> 00:04:22,500 ‫And let's call it y four star. 57 00:04:22,980 --> 00:04:27,390 ‫And of course, this entire vector, it's this one here. 58 00:04:27,930 --> 00:04:35,100 ‫So with that, you can extract all the use from all the predicted augmented state vectors. 59 00:04:35,730 --> 00:04:43,500 ‫And so in a compact way, you can write it all like this y global star, which is this one here. 60 00:04:44,130 --> 00:04:54,630 ‫It equals C Tilde Star Global, which is this gigantic matrix times x till their global. 61 00:04:55,020 --> 00:04:56,640 ‫Which is this one here?